Drift in low-cost lock-in amplifiers

The limitation on the performance of a lock-in amplifier imposed by noise and drift in the DC amplifier is discussed. Measurements on a commercial instrument show that if the time constant tau is increased whilst holding the ratio of tau to the scan time T fixed, the output noise first falls as tau -0.5, as expected for white noise, but then rises as tau 0.09. This shows that there is an optimal setting for the time constant beyond which the signal-to-noise ratio deteriorates, and suggests that the power density of the drift and noise from the DC amplifier in this instrument has an f-1.18 spectrum. The effect of both drift and noise may be reduced by signal averaging; if the number of scans n is varied while holding both the total measurement time nT and tau /T constant, the averaged RMS noise at first decreases as roughly 1/n, but not 1/n12/, before reaching a limiting value set by white noise. Replacing the first stage DC amplifier with an equivalent circuit based on a low-drift commutating auto-zero instrumentation amplifier reduces the drift and noise by up to a factor of four, and thus extends the useful range of time constants for single-scan measurements.